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Journal articles on the topic 'Multivariate discrete probability'

Author: Grafiati

Published: 9 March 2023

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1

Kafadar, Karen, Norman L. Johnson, Samuel Kotz, and N. Balakrishnan. "Discrete Multivariate Distributions." Journal of the American Statistical Association 92, no. 440 (1997): 1654. http://dx.doi.org/10.2307/2965453.

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2

Wiegand, Martin, Saralees Nadarajah, and Yuanyuan Zhang. "Discrete analogues of continuous multivariate probability distributions." Annals of Operations Research 292, no. 1 (2020): 183–90. http://dx.doi.org/10.1007/s10479-020-03633-5.

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3

Poston, Wendy L., Norman L. Johnson, Samuel Kotz, and N. Balakrishnan. "Discrete Multivariate Distributions." Technometrics 40, no. 2 (1998): 160. http://dx.doi.org/10.2307/1270659.

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4

Krummenauer, Frank. "Limit theorems for multivariate discrete distributions." Metrika 47, no. 1 (1998): 47–69. http://dx.doi.org/10.1007/bf02742864.

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5

Krummenauer, Frank. "Representation of multivariate discrete distributions by probability generating functions." Statistics & Probability Letters 39, no. 4 (1998): 327–31. http://dx.doi.org/10.1016/s0167-7152(98)00072-8.

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6

Vamvakari, Malvina. "On multivariate discrete q-Distributions-A multivariate q-Cauchy’s formula." Communications in Statistics - Theory and Methods 49, no. 24 (2019): 6080–95. http://dx.doi.org/10.1080/03610926.2019.1626427.

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7

Papageorgiou, H., N. L. Johnson, S. Kotz, and N. Balakrishnan. "Discrete Multivariate Distributions." Biometrics 54, no. 2 (1998): 795. http://dx.doi.org/10.2307/3109790.

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8

Rodríguez, J., A. Conde, A. J. Sáez, and M. J. Olmo. "On discrete multivariate distributions symmetric in frequencies." Test 12, no. 2 (2003): 459–80. http://dx.doi.org/10.1007/bf02595725.

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9

Chou, Jine-Phone. "Simultaneous Estimation in Discrete Multivariate Exponential Families." Annals of Statistics 19, no. 1 (1991): 314–28. http://dx.doi.org/10.1214/aos/1176347984.

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10

Zheng, Qi, and James H. Matis. "Approximating discrete multivariate distributions prom known moments." Communications in Statistics - Theory and Methods 22, no. 12 (1993): 3553–67. http://dx.doi.org/10.1080/03610929308831232.

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11

Barr, Aiala. "A multivariate model for discrete data sets." Communications in Statistics - Theory and Methods 18, no. 2 (1989): 445–59. http://dx.doi.org/10.1080/03610928908829910.

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12

Jones, M. C., and Éric Marchand. "Multivariate discrete distributions via sums and shares." Journal of Multivariate Analysis 171 (May 2019): 83–93. http://dx.doi.org/10.1016/j.jmva.2018.11.011.

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13

Teugels, J. L., and J. Van Horebeek. "Algebraic Descriptions of Nominal Multivariate Discrete Data." Journal of Multivariate Analysis 67, no. 2 (1998): 203–26. http://dx.doi.org/10.1006/jmva.1998.1764.

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14

Larntz, Kinley, Timothy R. C. Read, and Noel A. C. Cressie. "Goodness-of-Fit Statistics for Discrete Multivariate Data." Journal of the American Statistical Association 84, no. 408 (1989): 1101. http://dx.doi.org/10.2307/2290105.

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15

Zhou, Hua, and Kenneth Lange. "MM Algorithms for Some Discrete Multivariate Distributions." Journal of Computational and Graphical Statistics 19, no. 3 (2010): 645–65. http://dx.doi.org/10.1198/jcgs.2010.09014.

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16

Barbiero, Alessandro. "Estimating a multivariate model with discrete Weibull margins." Journal of Statistical Theory and Practice 11, no. 4 (2017): 503–14. http://dx.doi.org/10.1080/15598608.2017.1292483.

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17

Gupta, A. K., T. T. Nguyen, and Y. Wang. "A characterization of the multivariate discrete exponential family." Stochastic Analysis and Applications 18, no. 3 (2000): 417–27. http://dx.doi.org/10.1080/07362990008809678.

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18

Ip, Edward H., and Yuchung J. Wang. "Canonical representation of conditionally specified multivariate discrete distributions." Journal of Multivariate Analysis 100, no. 6 (2009): 1282–90. http://dx.doi.org/10.1016/j.jmva.2008.11.010.

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19

Ip, Ryan H. L., and K. Y. K. Wu. "A note on discrete multivariate Markov random field models." Statistics & Probability Letters 156 (January 2020): 108588. http://dx.doi.org/10.1016/j.spl.2019.108588.

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20

Komárek, Arnošt, and Lenka Komárková. "Clustering for multivariate continuous and discrete longitudinal data." Annals of Applied Statistics 7, no. 1 (2013): 177–200. http://dx.doi.org/10.1214/12-aoas580.

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21

Fasen-Hartmann, Vicky, and Markus Scholz. "Factorization and discrete-time representation of multivariate CARMA processes." Latin American Journal of Probability and Mathematical Statistics 19, no. 1 (2022): 799. http://dx.doi.org/10.30757/alea.v19-31.

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22

Richard Hansen, Niels. "Geometric ergodicity of discrete-time approximations to multivariate diffusions." Bernoulli 9, no. 4 (2003): 725–43. http://dx.doi.org/10.3150/bj/1066223276.

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23

Park, Taesung. "Multivariate regression models for discrete and continuous repeated measurements." Communications in Statistics - Theory and Methods 23, no. 6 (1994): 1547–64. http://dx.doi.org/10.1080/03610929408831339.

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24

Belaid, Nawal, Smail Adjabi, Célestin C. Kokonendji, and Nabil Zougab. "Bayesian adaptive bandwidth selector for multivariate discrete kernel estimator." Communications in Statistics - Theory and Methods 47, no. 12 (2017): 2988–3001. http://dx.doi.org/10.1080/03610926.2017.1346807.

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25

Nikoloulopoulos, Aristidis K., and Dimitris Karlis. "Finite normal mixture copulas for multivariate discrete data modeling." Journal of Statistical Planning and Inference 139, no. 11 (2009): 3878–90. http://dx.doi.org/10.1016/j.jspi.2009.05.034.

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26

Unnikrishnan Nair, N., and G. Asha. "Some Classes of Multivariate Life Distributions in Discrete Time." Journal of Multivariate Analysis 62, no. 2 (1997): 181–89. http://dx.doi.org/10.1006/jmva.1997.1682.

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27

Cacoullos, T. "Characterizations of generalized multivariate discrete distributions by a regression point." Statistics & Probability Letters 5, no. 1 (1987): 39–42. http://dx.doi.org/10.1016/0167-7152(87)90024-1.

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28

Fougeres, Anne-Laure, and Cecile Mercadier. "Risk Measures and Multivariate Extensions of Breiman's Theorem." Journal of Applied Probability 49, no. 2 (2012): 364–84. http://dx.doi.org/10.1239/jap/1339878792.

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The modeling of insurance risks has received an increasing amount of attention because of solvency capital requirements. The ruin probability has become a standard risk measure to assess regulatory capital. In this paper we focus on discrete-time models for the finite time horizon. Several results are available in the literature to calibrate the ruin probability by means of the sum of the tail probabilities of individual claim amounts. The aim of this work is to obtain asymptotics for such probabilities under multivariate regular variation and, more precisely, to derive them from extensions of Breiman's theorem. We thus present new situations where the ruin probability admits computable equivalents. We also derive asymptotics for the value at risk.

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29

Fougeres, Anne-Laure, and Cecile Mercadier. "Risk Measures and Multivariate Extensions of Breiman's Theorem." Journal of Applied Probability 49, no. 02 (2012): 364–84. http://dx.doi.org/10.1017/s0021900200009141.

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The modeling of insurance risks has received an increasing amount of attention because of solvency capital requirements. The ruin probability has become a standard risk measure to assess regulatory capital. In this paper we focus on discrete-time models for the finite time horizon. Several results are available in the literature to calibrate the ruin probability by means of the sum of the tail probabilities of individual claim amounts. The aim of this work is to obtain asymptotics for such probabilities under multivariate regular variation and, more precisely, to derive them from extensions of Breiman's theorem. We thus present new situations where the ruin probability admits computable equivalents. We also derive asymptotics for the value at risk.

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30

Maybank, S. J. "A multivariate distribution for sub-images." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2103 (2008): 983–1001. http://dx.doi.org/10.1098/rspa.2008.0212.

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A new method for obtaining multivariate distributions for sub-images of natural images is described. The information in each sub-image is summarized by a measurement vector in a measurement space. The dimension of the measurement space is reduced by applying a random projection to the truncated output of the discrete cosine transforms of the sub-images. The measurement space is then reparametrized, such that a Gaussian distribution is a good model for the measurement vectors in the reparametrized space. An Ornstein–Uhlenbeck process, associated with the Gaussian distribution, is used to model the differences between measurement vectors obtained from matching sub-images. The probability of a false alarm and the probability of accepting a correct match are calculated. The accuracy of the resulting statistical model for matching sub-images is tested using images from the Middlebury stereo database with promising results. In particular, if the probability of accepting a correct match is relatively large, then there is good agreement between the calculated and the experimental probabilities of obtaining a unique match that is also a correct match.

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31

Belaid, Nawal, Smail Adjabi, Nabil Zougab, and Célestin C. Kokonendji. "Bayesian bandwidth selection in discrete multivariate associated kernel estimators for probability mass functions." Journal of the Korean Statistical Society 45, no. 4 (2016): 557–67. http://dx.doi.org/10.1016/j.jkss.2016.04.001.

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32

Espeland, Mark A. "A general class of models for discrete multivariate data." Communications in Statistics - Simulation and Computation 15, no. 2 (1986): 405–24. http://dx.doi.org/10.1080/03610918608812515.

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33

Tsui, Kam-Wah. "Multiparameter estimation for some multivariate discrete distributions with possibly dependent components." Annals of the Institute of Statistical Mathematics 38, no. 1 (1986): 45–56. http://dx.doi.org/10.1007/bf02482499.

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34

Shih, Joanna H. "Modeling Multivariate Discrete Failure Time Data." Biometrics 54, no. 3 (1998): 1115. http://dx.doi.org/10.2307/2533861.

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35

Lim, Yaeji, Ying Kuen Cheung, and Hee-Seok Oh. "A generalization of functional clustering for discrete multivariate longitudinal data." Statistical Methods in Medical Research 29, no. 11 (2020): 3205–17. http://dx.doi.org/10.1177/0962280220921912.

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This paper presents a new model-based generalized functional clustering method for discrete longitudinal data, such as multivariate binomial and Poisson distributed data. For this purpose, we propose a multivariate functional principal component analysis (MFPCA)-based clustering procedure for a latent multivariate Gaussian process instead of the original functional data directly. The main contribution of this study is two-fold: modeling of discrete longitudinal data with the latent multivariate Gaussian process and developing of a clustering algorithm based on MFPCA coupled with the latent multivariate Gaussian process. Numerical experiments, including real data analysis and a simulation study, demonstrate the promising empirical properties of the proposed approach.

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36

Hoshino, Nobuaki. "A discrete multivariate distribution resulting from the law of small numbers." Journal of Applied Probability 43, no. 3 (2006): 852–66. http://dx.doi.org/10.1239/jap/1158784951.

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In the present article we derive a new discrete multivariate distribution using a limiting argument that is essentially the same as the law of small numbers. The distribution derived belongs to an exponential family, and randomly partitions positive integers. The facts shown about the distribution are useful in many fields of application involved with count data. The derivation parallels that of the Ewens distribution from the gamma distribution, and the new distribution is produced from the inverse Gaussian distribution. The method employed is regarded as the discretization of an infinitely divisible distribution over nonnegative real numbers.

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37

Smith, J. Q., and J. Croft. "Bayesian networks for discrete multivariate data: an algebraic approach to inference." Journal of Multivariate Analysis 84, no. 2 (2003): 387–402. http://dx.doi.org/10.1016/s0047-259x(02)00067-2.

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38

Song, Peter Xue-Kun. "Monte Carlo Kalman filter and smoothing for multivariate discrete state space models." Canadian Journal of Statistics 28, no. 3 (2000): 641–52. http://dx.doi.org/10.2307/3315971.

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39

Castro, Glaysar, and Valerie Girardin. "Characterization of periodically correlated and multivariate stationary discrete time wide Markov processes." Statistics & Probability Letters 78, no. 2 (2008): 158–64. http://dx.doi.org/10.1016/j.spl.2007.05.023.

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40

Manrique-Vallier, Daniel, and Jerome P. Reiter. "Bayesian Estimation of Discrete Multivariate Latent Structure Models With Structural Zeros." Journal of Computational and Graphical Statistics 23, no. 4 (2014): 1061–79. http://dx.doi.org/10.1080/10618600.2013.844700.

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41

Soltani, A. R., and M. Mohammadpour. "Time Domain Interpolation Algorithm for Innovations of Discrete Time Multivariate Stationary Processes." Stochastic Analysis and Applications 27, no. 2 (2009): 317–30. http://dx.doi.org/10.1080/07362990802678911.

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42

Steyn, H. S. "The fundamental importance of differential equations with three singularities in Mathematical Statistics." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 4, no. 1 (1985): 18–24. http://dx.doi.org/10.4102/satnt.v4i1.1012.

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It is well-known that the solution of a second order linear differential equation with at most five singularities plays a fundamental role in Mathematical Physics. In this paper it is shown that this statement also applies to Mathematical Statistics but with the difference that an equation with three singularities will suffice. Two wide classes of probability distributions are defined as solutions of such a differential equation, one for continuous distributions and one for discrete distributions. These two classes contain as members all the distributions which are normally considered as of importance in Mathematical Statistics. In the continuous case the probability functions are solutions of the relevant second order equation, while in the discrete case the probability generating functions are solutions there-of. By defining appropriate multidimentional extensions corresponding differential equations are obtained for continuous and discrete multivariate distributions.

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43

Khokhlov, Yu S. "Multivariate Analogs of Classical Univariate Discrete Distributions and Their Properties." Journal of Mathematical Sciences 234, no. 6 (2018): 802–9. http://dx.doi.org/10.1007/s10958-018-4047-y.

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44

Meinel, Nina. "Comparison of performance measures for multivariate discrete models." AStA Advances in Statistical Analysis 93, no. 2 (2008): 159–74. http://dx.doi.org/10.1007/s10182-008-0078-x.

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45

Shen, Chengwu, and Anh Ninh. "Finding the modes of some multivariate discrete probability distributions: Application of the resource allocation problem." Statistics & Probability Letters 156 (January 2020): 108579. http://dx.doi.org/10.1016/j.spl.2019.108579.

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46

SIRSI, SWARNAMALA. "SQUEEZING IN MULTIVARIATE SPIN SYSTEMS." International Journal of Modern Physics B 20, no. 11n13 (2006): 1465–75. http://dx.doi.org/10.1142/s0217979206034054.

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In contrast to the canonically conjugate variates q, p representing the position and momentum of a particle in the phase space distributions, the three Cartesian components, Jx, Jy, Jz of a spin-j system constitute the mutually non-commuting variates in the quasi-probabilistic spin distributions. It can be shown that a univariate spin distribution is never squeezed and one needs to look into either bivariate or trivariate distributions for signatures of squeezing. Several such distributions result if one considers different characteristic functions or moments based on various correspondence rules. As an example, discrete probability distribution for an arbitrary spin-1 assembly is constructed using Wigner-Weyl and Margenau-Hill correspondence rules. It is also shown that a trivariate spin-1 assembly resulting from the exposure of nucleus with non-zero quadrupole moment to combined electric quadrupole field and dipole magnetic field exhibits squeezing in certain cases.

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47

Omori, Yasuhiro, and Richard A. Johnson. "Efficient Semiparametric Bayesian Estimation of Multivariate Discrete Proportional Hazards Model with Random Effects." Communications in Statistics - Theory and Methods 38, no. 1 (2008): 29–41. http://dx.doi.org/10.1080/03610920802155478.

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48

Szántai, Tamás, and Edith Kovács. "Hypergraphs as a mean of discovering the dependence structure of a discrete multivariate probability distribution." Annals of Operations Research 193, no. 1 (2010): 71–90. http://dx.doi.org/10.1007/s10479-010-0814-y.

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49

Svensson, Åke. "On χ2-test of goodness-of-fit for a class of discrete multivariate models". Statistics & Probability Letters 3, № 6 (1985): 331–36. http://dx.doi.org/10.1016/0167-7152(85)90066-5.

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50

Azimmohseni, M., A. R. Soltani, and M. Khalafi. "Simulation of Real Discrete Time Gaussian Multivariate Stationary Processes with Given Spectral Densities." Journal of Time Series Analysis 36, no. 6 (2015): 783–96. http://dx.doi.org/10.1111/jtsa.12125.

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